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IV TABLE I. - Tangents and Externals to a 1° Curve. <br />Chord= 100 ft. <br />Int. <br />Angle <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />Angle <br />Tangent <br />External <br />43° <br />2257.0 <br />425.5 <br />50° <br />2671.8 <br />592.3 <br />01 <br />3110.9 <br />190,1 <br />10' <br />2266.6 <br />432.0 <br />10' <br />2681.9 <br />596.6 <br />10' <br />3121.7 <br />795.2 <br />20 <br />2276.2 <br />435.6 <br />20 <br />2692.1 <br />600.9 <br />20 <br />3132.6 <br />500.4 <br />30 <br />2285.9 <br />439.2 <br />30 <br />2702.3 <br />605.3 <br />30 <br />3143.4 <br />505.6 <br />40 <br />2295.6 <br />442.8 <br />40 <br />2712.5 <br />609.6 <br />40 <br />31.54.2 <br />810.9 <br />50 <br />2305.2 <br />446.4 <br />50 <br />2722.7 <br />614.0 <br />50 <br />3165.1 <br />S16.1 <br />44 <br />2314.9 <br />450.0 <br />51 <br />2732.9 <br />618.4 <br />58 <br />3176.0 <br />821.4 <br />10 <br />2324.6 <br />453.6 <br />10 <br />2743.1 <br />622.8 <br />10 <br />3186.9 <br />826.7 <br />20 <br />2334.3 <br />457.3 <br />- 20 <br />2753.4 <br />627.2 <br />20 <br />3197.8 <br />832.0 <br />30 <br />2344,1 <br />401.0 <br />30 <br />2763.7 <br />631.7 <br />30 <br />3208.8 <br />837.3 <br />iJ <br />2353.8 <br />464.6 <br />40 <br />2773.9 <br />636.2 <br />40 <br />3219.7 <br />842.7 <br />50 <br />'2363.5 <br />468.4 <br />50 <br />2754.2 <br />640.7 <br />50 <br />3230.7 <br />848.1 <br />45 <br />2373.3 <br />472.1 <br />52 <br />2794.:; <br />645.2 <br />59 <br />3241.7 <br />853.5 <br />10 <br />2383.1 <br />475.8 <br />10 <br />2804.9 <br />649.7 <br />10 <br />3252.7 <br />858.9 <br />20 <br />2392.8 <br />'479.620 <br />20 <br />281:1.2 <br />654.3 <br />20 <br />3263.7 <br />864.3 <br />30 <br />2402.6 <br />483.4 <br />30 <br />2825.6 <br />658.8 <br />30 <br />3274.8 <br />869.8 <br />40 <br />2412.4 <br />487.2 <br />40 <br />2835.9 <br />663.4 <br />403285.5 <br />4864.5 <br />• 875.3 <br />50 <br />2422.3 <br />491.0 <br />50 <br />2846.3 <br />668.0 <br />50 <br />3296.9 <br />850.8 <br />46 <br />2432.1 <br />494.8 <br />53 <br />2856.7 <br />672.7 <br />60 <br />3303.0 <br />SS6.4 <br />10 <br />2441.9 <br />498.7 <br />10 <br />2867.1 <br />677.3 <br />10 <br />3319.1 <br />892.0 <br />20 <br />2451.8 <br />502.5 <br />20 <br />2877.5 <br />682.0 <br />20 <br />3330.3 <br />897.5 <br />30 <br />2461.7 <br />506.4 <br />30 <br />2888.0 <br />686.7 <br />30 <br />3341.4 <br />903.2 <br />40 <br />2471.5 <br />510.3 <br />40 <br />2S9S.4 <br />691.4 <br />40 <br />3352.6 <br />908.8 <br />'50 <br />2481.4 <br />. 514.3 <br />50 <br />2908.9 <br />696.1 <br />50 <br />3363.8 <br />914.5 <br />47 <br />2491.3 <br />518.2 <br />64 <br />2919.4 <br />700.9 <br />61 <br />3375.0 <br />920.2 <br />10 <br />2501.2 <br />522.2 <br />10 <br />2929.9 <br />705.7 <br />10 <br />3336.3. <br />925.9 <br />20 <br />2511.2 <br />526.1 <br />20 <br />2940.4 <br />710.5 <br />20 <br />3397.5 <br />931.6 <br />30 <br />2521.1 <br />530.1 <br />30 <br />2951.0 <br />715.3 <br />30 <br />3408.8 <br />937.3 <br />40 <br />2531.1 <br />534.2 <br />40 <br />2961,5 <br />720.1 <br />40 <br />3420.1 <br />943.1 <br />50 <br />2541.0 <br />538.2 <br />50 <br />2972.1 <br />725.0 <br />50 <br />3431.4 <br />948.9 <br />48 <br />2551.0 <br />542.2 <br />55 <br />2982.7 <br />729.9 <br />62 <br />3442.7 <br />054.8 <br />10 <br />2561.0 <br />546.3 <br />10 <br />2993.3 <br />734.8 <br />10 <br />3454.1 <br />900.6 <br />20 <br />2571.0 <br />550.4 <br />20 <br />3003.9 <br />739.7 <br />20 <br />3465.4 <br />966.5 <br />30 <br />2581.0 <br />554.5 <br />30 <br />3014.5 <br />744.6 <br />30 <br />3476.8 <br />972.4 <br />40 <br />.2591.0 <br />558.6 <br />40 <br />3025.2 <br />749.0 <br />40 <br />3488.3 <br />978.3 <br />50 <br />2601.1 <br />562.8 <br />50 <br />3035.8 <br />754.6 <br />50 <br />3499.7 <br />984.3 <br />49 <br />2611.2. <br />566.9 <br />56 <br />3046.5 <br />759.6 <br />63 <br />3511.1 <br />990.2 <br />10 <br />2621.2 <br />571.1 <br />10 <br />3057.2 <br />764.6 <br />.10 <br />3522.6 <br />996.2 <br />20 <br />2631.3 <br />575.3 <br />20 <br />3067.9 <br />769.7 <br />20 <br />3534.1 <br />1002.3 <br />30 <br />2641.4 <br />579.5 <br />30 <br />3078.7 <br />774.7 <br />30 <br />3545.6 <br />1008.3 <br />40 <br />2651.5 <br />583.8 <br />40 <br />3089.4 <br />779.8 <br />40 <br />3557.2 <br />1014.4 <br />50 <br />2661.6 <br />538.0 <br />50 <br />3100.2 <br />784.9 <br />50 <br />3568.7 <br />1020.5 <br />Corrections to be Added (T =Tangent. E =External.) <br />Int. <br />Angle <br />Curve 5° <br />10° 15° 20° 25° 30° <br />35° 40° <br />45° 50° <br />55° 60° 65° 70° <br />40° <br />T=18 <br />.26 .40 .53 .67 .80 <br />.93 .108 <br />1.20 1.34 <br />1.49 1.64 1.79 1.94 <br />71.° <br />E =.023 <br />.046 ,070 .093 .117 ,141 <br />,172 .203 <br />.234 .255 <br />.277 .290 .315 .341 <br />451 <br />3501.9 <br />1032,8 <br />1218 1.254 <br />1.239 1325 .52 <br />1.351 1 2.411 .04 ? 21 <br />10' <br />E =.030 <br />060 .093 .109 .153 ,184 <br />20 <br />3603.5 <br />378 445 <br />50° <br />T=.17 <br />.34 .51 .68 .85 1.02 <br />1.19 1.36 <br />1.54 1.72 <br />1.91 2.10 2.29 2.48 <br />30 <br />E=.037 <br />.075 ,116 .151 ,169 ,227 <br />,266 .305 <br />345 384 <br />A25 .467 ,608 .550 <br />55° <br />T=.19 <br />.38 .57 .76 95 1.14 <br />1.32 1.62 <br />1.72 1.92 <br />2.14 2.35 2.56 2.77 <br />40 <br />E=.046 <br />.093 .142 .188 336 .283 <br />.332 3.81 <br />.420 .479 <br />.530 .582 .641 .700 <br />60° <br />T=•21 <br />,42 .63 84 1.05 1.27 <br />1.49 1.71 <br />1.94 2.17 <br />2.38 2.60 2.83 3.07 <br />50 <br />E =.050 <br />.112 .168 .225 .283 .340 <br />.398 .457 <br />.51G 575 <br />.'36 .697 .774 .851 <br />6S° <br />T=.23 <br />.46 69 93 1.16 1.40 <br />1.64 1.88 <br />2.13 2.38 <br />2.63 2.88 8.13 3.39 <br />10 <br />E=.067 <br />.135 204 .273 1 .343 .412 <br />,483 .554 <br />.625 .697 <br />.711 .845 .922 1.01 <br />TABLE I. - Tangents and Externals to a 1' Curve. <br />Chord =100 ft. <br />Int <br />Angle <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />Int' <br />Angle <br />Tangent <br />External <br />64° <br />3550.3 <br />1026,6 <br />71.° <br />4086.9 <br />1308.2 <br />78° <br />4639.8 <br />1643.0 <br />10' <br />3501.9 <br />1032,8 <br />10' <br />4099.5 <br />1315.6 <br />10' <br />4653.6 <br />1651.7 <br />20 <br />3603.5 <br />1039.0 <br />20 <br />4112.1 <br />1322.9 <br />20 <br />4667.4 <br />1660.5 <br />30 <br />3615.1 <br />1045.2 <br />30 <br />4124.8 <br />1330.3 <br />30 <br />4681.3 <br />1669.2 <br />40 <br />3626.8 <br />1051.4 <br />40 <br />4137.4 <br />1337.7 <br />40 <br />4695.2 <br />1678.1 <br />50 <br />3638.5 <br />1057.7 <br />50 <br />4150.1 <br />1345.1 <br />50 <br />4709.2 <br />1636.9 <br />65 <br />3650.2 <br />1063.9 <br />72 <br />4162.8 <br />1352.6 <br />79 <br />4723.2 <br />1695.8 <br />10 <br />3661.9 <br />1070.2 <br />10 <br />4175.6 <br />1360.1 <br />10 <br />4737.2 <br />1704.7 <br />20 <br />3673.7 <br />1076.6 <br />20 <br />4158.5 <br />1367.6 <br />20 <br />4751.2 <br />1713.7 <br />30 <br />3685.4 <br />1082.9 <br />30 <br />4201.2 <br />1375.2 <br />30 <br />4765.3 <br />1722.7 <br />40 <br />3697.2 <br />1089.3 <br />40 <br />4214.0 <br />1382.8 <br />40 <br />4770.4 <br />1731.7 <br />50 <br />3709.0 <br />1095.7 <br />50 <br />4226.8 <br />1390.4 <br />50 <br />4793.6 <br />1740.8 <br />66 <br />3720.9 <br />1102.2 <br />73 <br />4239.7 <br />1398.0 <br />80 <br />4807.7 <br />1749.9 <br />10 <br />3732.7 <br />1108.6 <br />10 <br />4252.0 <br />1405.7 <br />10 <br />4S22.0 <br />1759.0 <br />20 <br />3744.6 <br />1115.1 <br />20 <br />4265.0 <br />1413.5 <br />20 <br />.4836.2' <br />1768.2 <br />30 <br />3756.5 <br />1121.7 <br />30 <br />4278.5 <br />1421.2 <br />30 <br />4850.5 <br />1777.4 <br />40' <br />3768.5 <br />1128.2 <br />40 <br />4291.5 <br />1429.0 <br />40 <br />4864.5 <br />1786.7 <br />50 <br />3780.4 <br />1134.8 <br />50 <br />4304.6 <br />1436.8 <br />50 <br />4879.'2 <br />1796.0 <br />67 <br />3792.4 <br />1141.4 <br />74 . <br />4317.6 <br />1444.6 <br />81 <br />4893.6 <br />1505.3 <br />10 <br />3504.4 <br />1148.0 <br />10 <br />4330.7 <br />1452.5 <br />10 <br />4908.0 <br />1814.7 <br />20 <br />3816.4 <br />1154.7 <br />20 <br />4343.8 <br />1460.4 <br />20 <br />4922.5 <br />1524.1 <br />30 <br />3828.4 <br />1161.3 <br />30 <br />4356.9 <br />1463.4 <br />30 <br />4937.0 <br />1833.6 <br />40 <br />3840.5 <br />1168.1 <br />40 <br />4370.1 <br />1476.4 <br />1.40 <br />.4951.5 <br />1843.1 <br />50 <br />3852.6 <br />1174.8 <br />50 <br />4383.3 <br />1484.4 <br />50 <br />4900.1 <br />1852.6 <br />es <br />3864.7 <br />1181.6 <br />78 <br />4396.5 <br />1492.4 <br />82 <br />4980.7 <br />1S62.2 <br />10 <br />3876.8 <br />1188.4 <br />10 <br />4409.8 <br />1500.5 <br />10 <br />4995.4 <br />1871.8 <br />20 <br />3889.0 <br />1195.2 <br />20 <br />4423.1 <br />1508.6 <br />20 <br />5010.0 <br />1881.5 <br />30 <br />3901.2 <br />1202.0 <br />30 <br />4436.4 <br />1516.7 <br />30 <br />5024.8 <br />1891.2 <br />40 <br />3913.4 <br />1208.0 <br />.40 <br />.4449.7 <br />1524.9 <br />40 <br />5030.5 <br />1900.9 <br />50 <br />3925.6 <br />1215.8 <br />'50 <br />4463.1 <br />1533.1 <br />50 <br />5054.3 <br />1010.7 <br />69 <br />3937.9 <br />1222.7 <br />76 <br />4476.5 <br />1541.4 <br />83 <br />5069.2 <br />1920.5 <br />10 <br />3950.2 <br />1229.7 <br />10 <br />4459.9 <br />1549.7 <br />10 <br />503.1.0 <br />1930.4 <br />20 <br />3962.5 <br />1236.7 <br />20 <br />4503.4 <br />1558.0 <br />20 <br />5093.0 <br />1940.3 <br />30 <br />3974.8 <br />1243.7 <br />30 <br />4516.9 <br />1566.3 <br />30 <br />5113.9 <br />1950.3 <br />40 <br />3987.2 <br />1250.8 <br />40 <br />4530.4 <br />1574.7 <br />40 <br />5125.9 <br />1960.2 <br />50 <br />3999.5 <br />1257.9 <br />50 <br />4514.0 <br />1583.1 <br />50 <br />5143.9 <br />1970.3 <br />70 <br />4011.9 <br />1265.0 <br />77 <br />4557.6 <br />1591.6 <br />84 <br />5159.0 <br />1930.4 <br />10 <br />4024.4 <br />1272.1 <br />10 <br />4571.2 <br />1600.1 <br />10 <br />5174.1 <br />1990.5 <br />20 <br />4036.8 <br />-1279.3 <br />20 <br />4584.8 <br />1608.6 <br />20 <br />5159.3 <br />2000.6 <br />30 <br />4049.3 <br />12SG 5 <br />30 <br />4598.5 <br />1617.1 <br />30 <br />5204.4 <br />2010.8 <br />40 <br />4061.8 <br />1293.6 <br />40 <br />4612.2 <br />1625.7 <br />40 <br />5219.7 <br />2021.1 <br />50 <br />4074.4 <br />1300.9 <br />50 <br />4626.0 <br />1634.4 <br />50 <br />5234.9 <br />2031.4 <br />Corrections to be Added (T = Tangent. E = External.) <br />Curve 5° <br />10° <br />15° 20° <br />25° 30° <br />35° <br />40° <br />451 <br />501 <br />55° <br />60° <br />65° <br />70° <br />Angle <br />60° T=.21 <br />.42 <br />.63 .84 <br />1.05 1.27 <br />1.49 <br />1.71 <br />1.94 <br />2.17 <br />2.38 <br />2.60-2.83 <br />3.07 <br />E=.056 <br />.112 <br />.168 .225 <br />.283 .340 <br />.398 <br />.457 <br />.516 <br />.575 <br />.635 <br />,697 <br />,774 <br />,851 <br />65° <br />1.161 <br />1 <br />2.13 <br />2 <br />2 <br />2 <br />3 <br />E=.067 <br />.135 <br />.204 .273 <br />.343 .41 <br />1 2 <br />.483 <br />554 <br />.625 <br />697 <br />.71 1 <br />.845 <br />922 <br />1.01 - <br />70° T=.25 <br />.51 <br />.76 1.02 <br />1.28 1.54 <br />1.80 <br />2.06 <br />2.33 <br />2.60 <br />2.88 <br />3.16 <br />3.44 <br />3.72 <br />- E=.080 <br />.159 <br />.240 .321 <br />.403 .485 <br />.568 <br />.652 <br />.735 <br />.819 <br />.908 <br />.994 <br />1.08 <br />1.17 <br />75° T=.27 <br />.56.83 <br />1.12 <br />1.40 169 <br />L08 <br />2.27 <br />2.57 <br />2.87 <br />3.16 <br />3.47 <br />3.78 <br />4.09 <br />E=.095 <br />.182 <br />.286 .383 <br />.480 .578 <br />678 <br />.777 <br />.877 <br />.977 <br />1.07 <br />1.18 <br />1.29 <br />1.39 <br />SOP T=.30 <br />.61 <br />91 1.22 <br />1.53 1.84 <br />2.15 <br />2.46 <br />2.78 <br />3.10 <br />3.44 <br />3.78 <br />4.12 <br />4.46 <br />E=.110 <br />.220 <br />332 .445 <br />.558 .671 <br />.787 <br />.903 <br />1.03 <br />1.13 <br />1.25 <br />1.38 <br />1:50 <br />1.62 <br />85° T=.33 <br />.66 <br />1.00 1.33 <br />1.68 2.02 <br />2.36 <br />2.70 <br />3.05 <br />3.40 <br />3.77 <br />4.14 <br />4.55 <br />4.89 <br />E=.126 <br />.259 <br />.391 .524 <br />.657 .790 <br />.926 <br />1.08 <br />1.20 <br />1.34 <br />1.47- <br />1.82 <br />1.78 <br />1.91 <br />